Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #24923993 | C2 | semidirect |
| 2. #24923934 | C2 | semidirect |
| 3. #24923630 | C2 | semidirect |
| 4. #24923562 | C2 | semidirect |
| 5. #24923546 | C2 | semidirect |
| 7. #24923471 | C2 | semidirect |
| 8. #24923399 | C2 | semidirect |
| 9. #24923372 | C2 | semidirect |
| 11. #487×C167 | C2 | semidirect |
| 122. C167 | #3367 | semidirect |
| 127. #487 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923993 | 2 |
| #24923934 | 2 |
| #24923630 | 2 |
| #24923562 | 2 |
| #24923546 | 2 |
| #24923487 | 2 |
| #24923471 | 2 |
| #24923399 | 2 |
| #24923372 | 2 |
| C4×D1336 | 2 |
| #487×C167 | 2 |
| #3367 | 167 |